less bitcoins rewards will that make price go up?
It can if people view it as an increasing scarcity
Like oh there is only this many left I rather get in now mentality
(What happened last halving)
IMHO, block halving won't change the bitcoin supply too much. The daily number of new bitcoin will be dropped from 3,600 to 1,800, but the change is very small comparing with the total number of existing bitcoin.
While this may technically be true (in regards to coins being available), it does change something much bigger: profitability.
Let's say there are 100 coins minted per block and the average cost to mint a block is $100. The coins are currently worth $1 and the person breaks even. Great -- they're supporting the network.
Now the block halved. Coins are still $1, cost to mine a block is still $100. Now they are at a 50% loss on each block mined.
One of two things must happen: the price must go up to compensate people for mining or they are just going to stop.